NMR provides a very accessible technology for observing a wide variety of statistical quantum dynamics. Using NMR as a platform, we have demonstrated spinor behavior under rotations, the creation and validation of pseudo-pure states, the observation of "entangled" states, the implementation of the quantum Fourier transform and the realization of quantum logic gates. Simulations of wave function collapse using magnetic field gradients have also been performed. These experiments illustrate the basics of ensemble quantum computing and provide a means for further studies in quantum information processing.